We report on magneto-optical studies of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, a representative member of the 3D topological insulator family. Its electronic states in bulk are shown to be well described by a simple Dirac-type Hamiltonian for massive particles with only two parameters: the fundamental band gap and the band velocity. In a magnetic field, this model implies a unique property—spin splitting equal to twice the cyclotron energy: $E_s=2E_c$. This explains the extensive magnetotransport studies concluding a fortuitous degeneracy of the spin and orbital split Landau levels in this material. The $E_s=2E_c$ match differentiates the massive Dirac electrons in bulk ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ from those in quantum electrodynamics, for which $E_s=E_c$ always holds.

• Received 22 January 2015

DOI:https://doi.org/10.1103/PhysRevLett.114.186401